Heating, ventilation, and air conditioning (HVAC) systems move thermal energy between a low temperature environment and a high temperature environment in order to perform cooling or heating operations so that the comfort of the occupants in an indoor space can be maintained or improved. For example, heat can be moved from an indoor space to an outdoor space in order to lower the indoor temperature or mitigate the effect of thermal energy infiltrating an indoor space in a cooling operation. Conversely, heat can be moved from an outdoor space to an indoor space in order to raise the indoor temperature or mitigate the effect of thermal energy exfiltration an indoor space in a heating operation.
A multi-indoor unit HVAC system includes at least a single compressor and single outdoor heat exchanger connected to multiple indoor heat exchangers arranged in one or more indoor units. Refrigerant flow is split among the indoor units and modulated with flow metering valves arranged between the indoor heat exchangers and outdoor heat exchanger. These flow metering valves can also serve as the main pressure reducing device required to lower the refrigerant temperature and pressure in order to complete the vapor compression cycle. Depending on the state of a four-way valve connected to the compressor, high pressure refrigerant can flow from the compressor to the outdoor unit (in which case the outdoor unit heat exchanger is a condenser and the indoor unit heat exchangers are evaporators) or refrigerant can flow from the compressor to the indoor units and the roles of the indoor and outdoor heat exchangers are reversed.
Recent advancements in power electronics and low cost micro-controllers have led to variable speed compressors, electronically controlled valves, and variable speed fans. The control of these actuators must be coordinated to achieve room temperature regulation and enforce machine limitations such as a maximum safe pressure of the refrigerant or a maximum safe temperature of a system component.
One challenge for controller HVAC systems is that the system dynamics are modeled by very high-dimensional models, especially when the number of indoor units is large, for instance when regulating the temperatures in an office building. This makes controller generation very time and resource consuming since the numerical complexity of generating controllers grows non-linearly with model dimension. For instance, a popular method for generating controllers is using linear matrix inequalities (LMI). However, generating a controller using LMI based techniques for a moderately sized building with 50 indoor units requires up to 41 hours of computation. This issue is compounded by the fact that controller generation is typically an iterative process in which an engineer generates a controller, tests the controller, and then tweaks some of the design parameters to generates an improved controller.
There is a need for a system and method for generating controllers for large-scale HVAC systems that has low computational complexity while preserving the desired properties of the resulting controller.